1. Field of the Invention
The invention relates to a digital signal processing system comprising an analysing filter bank for dividing an incoming signal sampled at a rate f.sub.e and occupying a frequency band limited to f.sub.e /2, into N contiguous subband signals having a bandwidth of f.sub.e /2N and being sampled at the rate f.sub.e /N, and a synthesizing filter bank for recovering said incoming signal from said subband signals, said filter banks being formed by modulating a prototype low-pass filter having a finite and symmetrical impulse response, having a beginning-of-attenuation-band frequency f.sub.a less than f.sub.e /2N and satisfying the condition H.sup.2 (f)+H.sup.2 (f.sub.e /2N-f)=1 in the band of frequencies f extending from 0 to f.sub.a, where H(f) is the absolute value of the frequency response, modulating the prototype filter being effected by N sinusoidal modulation signals which, for forming the k-th subband (k extending from 0 to N-1), are characterized by the frequency f.sub.k =(2k+1)f.sub.e /(4 N), by the phase .alpha..sub.k for the analysing bank and by the phase -.alpha..sub.k for the synthesizing bank, the phase .alpha..sub.k being such that for the subband of the order k=0 the phase .alpha..sub.o =.pi./4, 3.pi./4, 5.pi./4 or 7.pi./4 and such that for two contiguous subbands of the order k and k-1 the difference .alpha..sub.k -.alpha..sub.k-1 =.pi./2 or -.pi./2.
2. Prior Art
Such systems comprising a cascade arrangement of an analysing bank and a synthesizing bank may be employed for, for example, reduced-rate encoding of a speech signal by quantizing the subband signals produced by the analysing bank with a number of variable levels depending on the energy of each subband signal.
In order to reduce the complexity of the filters in the considered filter banks, the filters are given comparatively wide transition bands which partly overlap for contiguous filters. The result of this is that the recovered signal coming from the synthesizing bank can be affected by spurious components due to the inevitable spectral folding (aliasing), which have an annoying level.
It is possible to avoid the influence of this spectral folding by an appropriate choice of the corresponding filter couples of the analysing and synthesizing banks.
This possibility has been demonstrated for filter banks having two subbands and has been extended to filter banks having a number of subbands equal to a power of two, thanks to the use of special half-band filters: for this subject see the article by A. Croisier, D. Esteban and C. Galand, "Perfect Channel Splitting by Use of Interpolation/Decimation, Tree Decomposition Techniques", published in the Proceedings of the International Conference on Information Sciences and Systems, pages 443-446, Patras, August, 1976. But, besides the fact that this procedure is limited as regards the possible number of subbands, it requires a comparatively large number of calculations and memories.
For effectively realizing filter banks, there is a technique originally developed in transmultiplexer systems and consisting in using for a filter bank a structure constituted by a polyphase network associated with a fast Fourier transform: for this subject reference is made to the article by M. G. Bellanger and J. L. Daguet, "TDM-FDM Transmultiplexer: Digital Polyphase and FFT", published in IEEE Trans. on Commun., Vol. COM-22, No. 9, September, 1974. It should be noted that, in this application, the subbands to be realized are disjunct and the spectral folding problem is avoided by means of filters having a narrow transition band which is situated between the subbands.
A technique of the type used in transmultiplexer systems but suitable for realizing the analysing and synthesizing filter banks of the system now under consideration, that is to say providing subbands which are not disjunct, has been studied for certain specific cases by J. H. Rothweiler in the article "Polyphase Quadrature Filters--A New Subband Cooling Technique" published in Proc. ICASSP 83, Boston, pages 1280-1283, and by H. H. Nussbaumer and M. Vetterli in the article "Computationally Efficient QMF Filter Banks" published in Proc. ICASSP 84, San Diego, pages 1131-1134. For these specific cases, the number of subbands generally is a power of two and the number of coefficients of each filter of the filter bank is a multiple of the number of subbands and, in an implementation utilizing a polyphase network and a Fourier transform, this implies the use of a same even number of coefficients in all the branches of the polyphase network.